"The bear is writing a long love letter to the girl, because it thinks she is so beautiful."
Translation:Bjørnen skriver et langt kærlighedsbrev til pigen, fordi den synes hun er så smuk.
Yes, as far as I understand, the usage of at with synes is optional; it can be ommitted. But it should be correct when it is not ommited. So it should be accepted.
I have checked many sentences given by Duolingo, here are two of them: One with at and the other without at, when the synes structure is before a whole sentence:
Does anyone know for sure?